Despite kicking 14 points, Jackson's radar was not always functioning smoothly as he missed three first-half penalties.
All the Scarlets' points came from the boot of Dan Newton but shorn of their Welsh internationals the visitors failed to click as an attacking unit.
With the teams sat fourth and fifth heading into the match, it was little surprise the first half was an incredibly tight affair at Firhill.
Both Jackson and Newton were off target with penalties in the opening ten minutes before the former did open his account when the Scarlets came in from the side on 14 minutes.
The hosts were dominating possession and territory but after 13 rounds of competition the Scarlets showed exactly why they have the best defensive record with some thundering hits and turnovers.
Jackson was again off target with a longer-range penalty and further blotted his copybook when he conceded a penalty that allowed Newton to level the scores.
It took a moment of invention from Samoan winger David Lemi to nearly break the try deadlock when his chip and chase nearly resulted in a score, but the TMO ruled Gareth Davies got the first touch of the ball.
There were more worrying moments for the Scarlets coaching staff shortly afterwards when Iestyn Thomas departed the field with a suspected neck injury on 29 minutes.
Just two minutes later, Glasgow finally got the try their superiority merited when they were camped on the Scarlets line and Welsh burrowed over from close range.
Jackson converted but in a shaky half for the Scotland fly-half he botched his third penalty more or less straight in front of the posts to leave the halftime score 10-3.
Despite the Scarlets making a bright start to the second half, a break by David Lemi had the visitors scrambling in defence and conceded a penalty which Jackson converted only for Newton to immediately reply to keep it a seven-point game.
The kickers exchanged a further penalty apiece before Jackson nudged the Scarlets out of bonus-point territory with his fourth penalty with ten minutes to go.
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|Scarlets Score Card|